Solve for $x$ and $y$ using elimination. ${2x-y = 3}$ ${5x+y = 25}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $7x = 28$ $\dfrac{7x}{{7}} = \dfrac{28}{{7}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {2x-y = 3}\thinspace$ to find $y$ ${2}{(4)}{ - y = 3}$ $8-y = 3$ $8{-8} - y = 3{-8}$ $-y = -5$ $\dfrac{-y}{{-1}} = \dfrac{-5}{{-1}}$ ${y = 5}$ You can also plug ${x = 4}$ into $\thinspace {5x+y = 25}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ + y = 25}$ ${y = 5}$